3. Resistance of a Ship
3.2 Estimates based on statistical methods
• In the preliminary stages of ship design, the resistance
coefficient is estimated with approximate methods based
on systematic series or statistical regressions to
experimental data.
• A systematic series is a family of ship hulls obtained from
a systematic variation of one or more shape parameters.
Usually, the changes are based on a parent form. The
resistance of all the models that constitute a series is
measured experimentally. This database allows the
interpolation of the resistance coefficient for other shapes
originated by parametric variations of the original shape
1
3. Resistance of a Ship
3.2 Estimates based on statistical methods
• The Froude number is related to the fineness coefficient.
Ships with a high Froude number exhibit a resistance
coefficient dominated by the wave resistance and have a
smaller fineness coefficient.
• The longitudinal distribution of the displacement affects
the resistance and is related to the Froude number. This
distribution is caracterized by the buoyancy centre. For
ships with low Froude number, the resistance is dominated
by the flow separation region that might occur at the stern.
2
3. Resistance of a Ship
3.2 Estimates based on statistical methods
• The risk of flow separation is reduced if the buoyancy
centre is upstream of midship. In the case of high Froude
numbers, wave resistance dominates the resistance
coefficient. In these cases, the crictical region is the bow,
which should be thinner moving the buoyancy centre to a
location downstream of midship.
• The vertical displacement is influenced by the choice of V
or U sections. U shaped sections lead to smaller wave
resistance than V shapes, but to highest risk of flow
separation.
3
3. Resistance of a Ship
3.2 Estimates based on statistical methods
Taylor series
• Taylor performed model tests (between 1907 and 1914) for
systematic variations of a parent form defined by the
British cruiser “Leviathan”.
• Systematic variations of models shape:
– 5 ratios length/displacement1/3: L / ∆1 / 3
– 3 ratios beam/draft: B / T 2,25, 2,92 e 3,75
– 8 prismatic coefficients: C p from 0,48 a 0,86
– Only 2 values of B/T 2,25 and 3,75 were used by
Taylor: 80 models.
3
C R = f (V / Lwl , B / T , C p , ∆ / Lwl )
4
3. Resistance of a Ship
3.2 Estimates based on statistical methods
Taylor series
• Reanalysis of the results by Gertler (1954).
– Corrections for water temperature, laminar flow and
blockage.
– Viscous resistance from Schoenherr line. Froude’s
method. Results give residual resistance.
– B/T=2,92 was converted to 3.
– 117 diagrams of residual resistance.
C R = f (V / Lwl , B / T , C p , ∆ / Lwl 3 )
5
3. Resistance of a Ship
•
•
•
•
3.2 Estimates based on statistical methods
Taylor series
Taylor’s parent form.
Fineness coefficient of main section 0,925.
Hull centre at midship.
Stern for two propellers.
6
3. Resistance of a Ship
3.2 Estimates based on statistical methods
Taylor series
7
3. Resistance of a Ship
3.2 Estimates based on statistical methods
Other series
• Série 60 (Todd, 1960)
– Single screw merchant ship
– 5 parent forms with fineness coefficients: 0,60, 0,65,
0,70, 0,75 and 0,80.
– For each fineness coefficient, the location of the hull
centre was optimized.
– Variations of L/B, B/T, etc.
• Other series include BSRA, SSPA, NPL,...
8
3. Resistance of a Ship
3.2 Estimates based on statistical methods
Method of Holtrop and Mennen
• The method estimates the resistance of displacement ships.
• Statistical regression of model tests and results from ship
trials.
• The database covers a wide range of ships. For extreme
shapes the number of cases in the database is small.
Therefore, the accuracy of the estimates is worse.
• The method may be used to assess qualitatively the
resistance of a ship design.
9
3. Resistance of a Ship
3.2 Estimates based on statistical methods
Method of Holtrop and Mennen
• Two formulations:
– Standard method – Method of Holtrop and Mennen: J.
Holtrop, “A statistical re-analysis of resistance and
propulsion data”, ISP, Vol. 31, No. 363, November
1984.
– “Improved” method: J. Holtrop, “A statistical resistance
prediction method with a speed dependent form factor”,
SMSSH’88, Varna, Oct. 1988.
10
3. Resistance
Ship estatísticos
3.2 Previsão da resistência
do navio of
comamétodos
3.2 Estimates
based
on estatistical
Método de
Holtrop
Mennen methods
Method of Holtrop and Mennen
• Resistance decomposition:
RT = (1 + k1 ) R F + Rw + R B + RTR + R APP + R A
RT
RF
1 + k1
Rw
RB
=
=
=
=
=
Total resistance
Friction resistance from the ITTC 1957 line
Form factor of bare hull
Wave resistance of bare hull
Wave resistance of the bulbous bow
11
3. Resistance
Ship estatísticos
3.2 Previsão da resistência
do navio of
comamétodos
3.2 Estimates
based
on estatistical
Método de
Holtrop
Mennen methods
Method of Holtrop and Mennen
• Resistance decomposition:
RT = (1 + k1 ) R F + Rw + R B + RTR + R APP + R A
RTR = Additional resistance from the immersed
Transom
R APP = Appendage resistance
RA
= Correlation allowance
.
12
3. Resistance of a Ship
3.2 Estimates based on statistical methods
3
1
+
k
=
f
(
L
/
B
,
L
/
T
,
LCB
,
∇
/
L
,C p )
1
Method of Holtrop and Mennen
• Form factor of bare hull:
1 + k1 = f ( L / B, L / T , LCB, ∇ / L3 , C p )
• Wave resistance:
Rw
= f ( Fn , C M , ∇ / L3 , L / B, B / T , ABT / BT , AT / BT , T f , hb , C p )
∇ρg
∇
= Displacement
CM
L
B
T
LCB
=
=
=
=
=
Fineness coefficient
Length at fluctuation
Beam
Draft
Longitudinal position of hull centre
13
3. Resistance of a Ship
3.2 Estimates based on statistical methods
3
1
+
k
=
f
(
L
/
B
,
L
/
T
,
LCB
,
∇
/
L
,C p )
1
Method of Holtrop and Mennen
• Wave resistance:
Rw
= f ( Fn , C M , ∇ / L3 , L / B, B / T , ABT / BT , AT / BT , T f , hb , C p )
∇ρg
Cp
= Prismatic coefficient
AT
ABT
Tf
hb
Fn
= Tranversal section of transom at rest
= Transversal section of bulbous bow
= Vertical distance from the bulbous section
centre to the keel line (m)
= Draft at the bow (m)
= Froude number
14
3.2 Previsão da resistência
do navio of
comamétodos
3. Resistance
Ship estatísticos
Método de
Holtrop
Mennen methods
3.2 Estimates
based
on estatistical
Method of Holtrop and Mennen
• Regression formula for the wetted surface
S = f ( L, B, T , C M , Cb , C wp , ABT )
–
C wp
Fineness coefficient at fluctuation
R APP =
1
ρV 2 S APP (1 + k 2 )C F
2
• Additional resistance of the bulb depending on bulb
characteristics and its immersion.
15
3.2 Previsão da resistência
do navio of
comamétodos
3. Resistance
Ship estatísticos
Método de
Holtrop
Mennen methods
3.2 Estimates
based
on estatistical
Method of Holtrop and Mennen
• Resistance of the appendages
1
R APP = ρV 2 S APP (1 + k 2 )C F
2
– V
=
– S APP =
– 1 + k2 =
– CF =
Ship speed
Wetted surface of the appendages
Form factor of the appendages
Friction resistance coefficient of the ship
16
3.2 Previsão da resistência
do navio of
comamétodos
3. Resistance
Ship estatísticos
Método de
Holtrop
Mennen methods
3.2 Estimates
based
on estatistical
Method of Holtrop and Mennen
• Resistance of the immersed area of the transom AT and of
other parameters related to the immersed transom
• Correlation allowance for the model-ship extrapolation
RA =
1
ρV 2 SC a
2
– The correlation allowance depends on L and other
parameters
17
3.2 Previsão da resistência
do navio of
comamétodos
3. Resistance
Ship estatísticos
Método
Melhorado
3.2 Estimates
based
on statistical methods
Improved method of Holtrop and Mennen
• Differences to the standard method
– Form factor depending on the ship speed
– Revised formulas for the wave resistance
– Separate relations for the air resistance. In the standard
method it was included in the correlation allowance
• Other improvements:
– Added resistance due to incoming waves
– Added resistance from head wind
– Shallow water corrections
18